Hydrogen Burning Nucleosynthesis, Classical Novae, and X-Ray...
Transcript of Hydrogen Burning Nucleosynthesis, Classical Novae, and X-Ray...
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Lecture 9
Hydrogen Burning Nucleosynthesis, Classical Novae, and X-Ray Bursts
red = slow
, , ,( ) ( )I I j jk L k kj
j k k j L L k I j
dY Y Y I Y Y Ldt
ρ λ ρ λ∍ + = +
= − +∑ ∑
Once the relevant nuclear physics is known in terms of the necessary rate factors, = NA = f(T,), the evolution of the composition can be solved from the coupled set of rate equations:
The rather complicated looking restriction on the second summation simply reflects the necessary conservation conditions for the generic forward reaction, I(j,k)L and its reverse, L(k,j)I. k and j are typically n, p, , or . In the special case of weak decay one substitutes for Yj $ the inverse mean lifetime against the weak interaction, = 1/beta. The mean lifetime is the half-life divided by ln 2 = 0.693. Then one has a term with a single Yi times .
(actually one would need to worry about other reactions that might affect the abundance of either, but this is just an example to make a point)
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And, if the entire cycle were in steady state
Then
Everywhere that dYidt
≈ 0
i.e., Y (14N )
Y (12C)= Y (
14N )Y (13C)
⎛⎝⎜
⎞⎠⎟Y (13C)Y (12C)
⎛⎝⎜
⎞⎠⎟=
λpγ (13C)
λpγ (14N )
⎛
⎝⎜⎞
⎠⎟λpγ (
12C)λpγ (
13C)⎛
⎝⎜⎞
⎠⎟
if all three isotopes are in steady state
That is, the ratio of the abundances of any two species in steady state is the inverse
ratio of their destruction rates
How long does it take for a pair of nuclei to reach steady state? The time to reach steady state is approximately the reciprocal of the destruction rate for the more fragile nucleus.
Eg. for 13C [absorb ρYp into λ for simplicity];
i.e. λ12 = ρYpλ pγ (12C); λ13= ρYpλ pγ (
13C)]
dY13dt
= −Y13λ13 +Y12λ12dY12dt
≈ −Y12λ12
Let u = Y13 / Y12 then
dudt
= 1Y12
dY13dt
−Y13Y12
2
dY12dt
= λ12 −Y13Y12
λ13+Y13Y12
λ12
= λ12 + u (λ12 −λ13)
Integrating and assuming Y13=0 at t = 0 and
Y13
Y12
=λ
12
λ13
after a time τss= time required to reach steady state, one
has with some algebra
τss=
lnλ
12
λ13
⎛
⎝⎜⎞
⎠⎟
λ12−λ
13( )
which says steady state will be reached on the faster of the
two reaction time scales, 1/λ12
or 1/λ13
nb. always > 0 since ln of a number < 1 is negative
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* fastest at 30
At T6 = 30 ρYp =100
ρYpλ pγ (13C)( ) −1 = 1.5×108 sec 12C ↔13 C (2nd quick)
ρYpλ pγ (15 N )( )−1 = 1.4×106 sec !5N↔ 14N (quickest)
ρYp λ pα (17 O)( )−1 = 2.9×1011 sec 17O ↔ 16O (slow)
ρYpλ pγ (14 N )( )−1 = 4.2 × 1010 sec one cycle of the main CNO cycle
ρYpλ pγ (16O)( )−1= 1.6 × 1012 sec 16O↔ 14N (slow)
ρYpλ pγ (12C)( )−1 = 5.6 × 108 sec 12C ↔14 N (quick)
Steady state after several times these time scales.
= 1 to 10 would be more appropriate for massive stars where T is this high, so the real time scale should be about 10 times greater. Also lengthened by convection.
1% C; 1% O Provided steady state has been achieved the abundance ratios are just given by the s.
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Giant stars in the globular cluster M4
Suntzeff and Smith
(ApJ, 381, 160, (1991))
Will have to make 15N somewhere else not in steady state with 14N
13C14 N
⎞⎠⎟
= 0.035 T6
13C14 N
⎞⎠⎟SS
=λpγ (
14 N)
λpγ (12 C)
20 2.0(-3)
30 7.9(-3)
40 7.7(-3)
So one can make 13C
12C
large but cannot make 13C
14N
big compared with its solar value. Cardinal rule of
nucleosynthesis - you must normalize to your
biggest overproduction, nitrogen in this case.
Way out: Make 13C in a CN process that has not reached steady state (because of the longer life of 13C(p,)14N, e.g., make 13C in a region where just a few protons are mixed in with the carbon and then convection cools the material.
Hydrogen Burning Nucleosynthesis Summary
12C - destroyed by hydogen burning. Turned into 13C if incomplete cycle. 14 N otherwise.13C - produced by incomplete CNcycle. Made in low mass stars. Ejected in red giant winds and planetary nebulae14N - produced by the CNO cycle from primordial 12C and 16O present in the star since its birth. A secondary element. Made in low mass (M < 8 M) stars and ejected in red
giant winds and planetary nebulae. Exception: Large quantities of "primary" nitrogen can be made in very massive stars when the helium convective core encroaches on the hydrogen envelope.
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15N - Not made sufficiently in any normal CNO cycle> Probably made in classical novae as radioactive 15O16O - Destroyed in the CNO cycle. Made in massive stars by helium burning17O - Used to be made in massive stars until the rate for 17O(p,α )14N was remeasured and found to be large. probably made in classical novae18O - made in helium burning by 14N(α,γ )18F(e+ν)18O23Na - Partly made by a branch of the CNO cycle but mostly made by carbon burning in massive stars.26 Al - long lived radioactivity made by hydrogen burning but more by explosive neon burning in massive stars
Hydrogen burning under extreme conditions
Scenarios:
• Hot bottom burning in massive AGB stars (> 4 solar masses) (T9 ~ 0.08)
• Nova explosions on accreting white dwarfs (T9 ~ 0.4)
• X-ray bursts on accreting neutron stars (T9 ~ 1 - 2)
• accretion disks around low mass black holes ? • neutrino driven wind in core collapse supernovae ?
14O (p,)%(e+)
Slowest rates are weak decays of 14O and 15O.
Suppose keep raising the temperature of the CNO cycle. Is there a limit how fast it can go? Eventually one gets hung up on the finite life times for 14O (70.6 s) and 15O (122 s) to decay by positron emission. This has several interesting consequences:
• Material accumulates in 14O and 15O rather than 14N, with interesting nucleosynthetic consequences for 15N. But can the material cool down fast enough that 15N is not destroyed by 15N(p,)12C in the process?
• The nuclear energy generation rate becomes temperature insensitive and exceptionally simple
• As the temperature continues to rise matter can eventually break out of 14O and 15O especially by the reaction 15O(,)19Ne(p,)20Na(p,)21Mg(e+) ….
The rp-process.
εnuc
=5.9×1015 Z erg g−1 s−1
The -limited CNO cycle
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3 4 5 6 7 8
9 10
111213
14
C (6) N (7)
O (8) F (9)
Ne (10)Na (11)
Mg (12)
3 4 5 6 7 8
9 10
111213
14
C (6) N (7)
O (8) F (9)
Ne (10)Na (11)
Mg (12)
Cold CN(O)-Cycle
Hot CN(O)-Cycle
),(14 γσε pNv >∝<Energy production rate:
T9 < 0.08
T9 ~ 0.08-0.1
const)/(1 11)(15)(14=+∝ −−
++ ββλλε
OO
beta limited CNO cycle
Note: condition for hot CNO cycle depend also on density and Yp:
βγ λλ >,pon 13N:
βλσρ >>~ 0.3 15O(,)19Ne 18Ne(,p)21Na T9 >~ 0.6
0.0 0.5 1.0 1.5100
101
102
103
104
105
Temperature (GK)
Den
sity
(g/c
m3 )
Multizone Nova model (Starrfield 2001)
Breakout
No Breakout
Breakout depends on uncertain rate for 15O(,)19Ne
Classical Novae • Distinct from dwarf novae which are probably accretion disk instabilities • Thermonuclear explosions on accreting white dwarfs. Unlike supernovae, they recur, though generally on long (>1000 year) time scales. • Rise in optical brightness by > 9 magnitudes • Significant brightness change thereafter in < 1000 days • Evidence for mass outflow from 100 s to 5000 km s-1 • Anomalous (non-solar) abundances of elements from carbon to sulfur
One place where the -limited CNO cycle is important is classical novae. Another is in x-ray bursts on neutron stars.
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• Typically the luminosity rises rapidly to the Eddington luminosity for one solar mass (~1038 erg s-1) and stays there for days (fast nova) to months (slow nova) • In Andromeda (and probably the Milky Way) about 40 per year. In the LMC a few per year. • Evidence for membership in a close binary – 0.06 days (GQ-Mus 1983) 2.0 days (GK Per 1901) see Warner, Physics of Classical Novae, IAU Colloq 122, 24 (1990)
V1500 Cygni
Discovery Aug 29, 1975 Magnitude 3.0
A fast nova
Nova Cygni 1992
The brightest recent nova. Visible to the unaided eye (m = 4.4).
Photo at left is from HST in 1994. Discovered Feb. 19, 1992. Spectrum showed evidence
for ejection of large amounts of neon, oxygen, and magnesium,
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Fast nova – rise is very steep and the principal display lasts only a few days. Falls > 3 mag within 110 days
Slow nova – the decline by 3 magnitudes takes at least 100 days. There is frequently a decline and recovery at about 100 days associated with dust formation.
Very slow nova – display lasts for years.
Recurrent novae – observed to recur on human time scales. Some of these are accretion disk instabilities
Effect of embedded companion star?
Red dwarf stars are very low mass main sequence stars
An earth mass or so is ejected at speeds of 100s to 1000s of km/s. Years later the ejected shells are still visible. The next page shows imgaes from a ground-based optical survey between 1993 and 1995 at the William Hershel Telescope and the Anglo-Australian Telescope.
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Nova Cygni (1975) V1500 Cygni
Nova Serpentis (1970) FH Ser
Nova Pictoris (1927) RR Pic
Nova Hercules (1934) DQ - Her
Nova Persei (1901) GK Per
http://www.jb.man.ac.uk/~tob/novae/
4
2
. ., ;44
dP GMi edm rdm r dr
ππ ρ
=
=
Models
A white dwarf composedof either C and O (< 1.06 M )
or O, Mg, and Ne (> 1.06 M )accretes hydrogen-rich
material from a companion star at a rate of 10-9±1 M / yr
As the matter piles up, it becomes dense and hot. It is heatedat its base chiefly by gravitational compression, though thetemperature of the white dwarf itself may play a role.
Ignition occurs at a critical pressure of 2 × 1019 dyne cm-2 (Truran and Livio 1986);basically this is the condition that Tbase ~10
7 K
This implies a certain critical mass since
ΔMign≈
4πPign
G
RWD
4
MWD
~ 10-5 -10-4 M
-1/3
Approximately,
R M∝
Models
RWD ≈8.5×108 1.286
MWDM
⎛
⎝⎜⎞
⎠⎟
−2/3
− 0.777MWDM
⎛
⎝⎜⎞
⎠⎟
2/3⎡
⎣⎢⎢
⎤
⎦⎥⎥
1/2
cm
Eggleton (1982) as quoted in Politano et al (1990)
This gives a critical mass that decreases rapidly (as M-7/3) with mass. Since the recurrence interval is this critical mass divided by the accretion rate, bursts on high mass white dwarfs occur more frequently
where we have used for the white dwarf radius:
The mass of the accreted hydrogen envelope at the time the hydrogen ignites is a function of the white dwarf mass and accretion rate.
Nomoto (1982)
For a given accretion rate
the critical mass is smaller for larger mass white dwarfs
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0.60 12.9 0.70 7.3 0.80 4.2 0.90 2.4 1.00 1.2 1.10 0.64 1.20 0.28 1.30 0.09 1.35 0.04
Even though the average mass white dwarf is 0.6 – 0.7 solar masses the most often observed novae have masses around 1.14 solar masses. These would be white dwarfs composed of Ne, O, and Mg. It is estimated that ~ 1/3 of novae, by number, occur on NeOMg WDs even though they are quite rare.
Mass WD Interval (105 yr)
Politano et al (1990) in Physics of Classical Novae
see also Ritter et al, ApJ, 376, 177, (1991)
Truran and Livio (1986) using Iben (1982) – lower limits especially for high masses For typical values:
MWD =1.0 MRWD ≈ 5500kmAccreted layer ΔR≈ 150 km
ΔM ≈4πR4Pcrit
GM=7×10−5 M
ρ ~ ΔM4πR2ΔR
3000 g cm-3
Partially degenerate at 107 K
Nature of the burning:
Confusing statements exist in the literature. A nova is not a degenerate flash that happens in seconds and then is over (like a SN Ia). The ignition is partly degenerate but actually resembles a thin shell instability more than a nuclear runaway. So long as the radius of the center of mass of the burning layer does not increase dramatically, the pressure at the base stays constant. Some expansion occurs but not enough to put the burning out. At constant P, when density goes down, T goes up. So the hydrogen continues to burn for a long time, dredging up C and O as it proceeds. Hydrostatic equilibrium maintains the luminosity at near the Eddington value. Matter is lost as a “super-wind”, not as a blast wave. The dredge up of C and O is very important to the energetics and nucleosynthesis
For the beta-limited CNO cycle
εnuc
= 5.9 × 1015 Z erg g-1 s-1 Z ~ 0.01 - 0.1
for M = 10-5 M
; Z = 0.01
L = εnuc
M ~ 1042 erg s-1
So the initial flash is quite super-Eddington, but that drives
convection and expansion until a smaller region is burning
and L~1038 −1039 erg s−1.
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The binding energy per gram of material at the white dwarf edge is about
GMR
≈6.67E − 8( ) 2E33( )
5E8≈ 2 ×1017 erg gm−1
So to eject e.g., 3 x 10-5 solar masses takes about 1046 erg. The kinetic energy (e.g., 1000 km/s) is about 1045 The integral of the Eddington luminosity for 107 s is also about 1045 erg. So the binding energy dominates the energy budget ad the light and kinetic energy are a small fraction of that. In some cases common envelope effects may also be important. The companion star is inside the nova.
Nucleosynthesis in Novae Basically 15N and 17O
The mass fraction of both in the ejecta is ~0.01, so crudely …
Mnova
(15O) ~ 0.01( ) 3×10−5( ) 30( ) 1010( ) ~ 105 MX
Pop I
15 N( ) ~ 105 / 3 × 1010 ~ 4× 10−6 ≈ the solar mass fraction of 15N and 17O in the sun.
Novae also make interesting amounts of 22Na and 26Al for gamma-ray astronomy
approximate Pop I material in the Galaxy within solar orbit
Woosley (1986)
Some issues
• Burning is not violent enough to give fast novae unless the accreted layer is significantly enriched with CNO prior to or early during the runaway. • Understanding luminosity – speed classes. Fast novae are brighter. • Relation to Type Ia supernovae. How to grow MWD when models suggest it is actually shrinking?
Shear mixing during accretion Convective undershoot during burst
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First X-ray burst: 3U 1820-30 (Grindlay et al. 1976) with ANS (Astronomical Netherlands Satellite)
T~ 5s
10 s
Type I X-Ray Bursts
• Burst rise times < 1 s to 10 s • Burst duration 10 s of seconds to minutes (some much longer “superbursts”) • Occur in low mass x-ray binaries • Persistent luminosity from
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(1735-444)
18 18.5 time (days)
(rapid burster)
(4U 1735-44)
Normal type I bursts: • duration 10-100 s • ~1039 erg
Superbursts: (discovered 2001, so far 7 seen in 6 sources) • ~1043 erg • rare (every 3.5 yr ?)
24 s
3 min
4.8 h
• Of 13 known luminous globular cluster x-ray sources, 12 show x-ray bursts. Over 70 total X-ray bursters were known in 2002. • Distances 4 – 12 kpc. Two discovered in M31 (Pietsch and Haberl, A&A, 430, L45 (2005). • Low B-field < 108-9 gauss • Rapid rotation (at break up? due to accretion?). In transition to becoming ms pulsars? • Very little mass lost (based upon models). Unimportant to nucleosynthesis
But 1 MeV/nucleon
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X-ray burst theory predicts (at least) two regimes of burning:
2≥
1)
2)
Radius expansion is also inferred from a decrease in Teff at constant L, but some of the L’s themselves are super-Eddington
Neutron Star Donor Star ( normal star)
Accretion Disk
The Model Neutron stars: 1.4 Mo, 10 km radius (average density: ~ 1014 g/cm3)
Typical systems: • accretion rate 10-8/10-10 Mo/yr (0.5-50 kg/s/cm2) • orbital periods 0.01-100 days • orbital separations 0.001-1 AU s
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Observation of thermonuclear energy:
Unstable, explosive burning in bursts (release over short time)
Burst energy thermonuclear
Persistent flux gravitational energy
Gravitational energy
Nuclear energy 30 − 40
Very little matter if any is ejected by
a x-ray burst. Nucleosynthetically sterile.
0 12
3 4 5
67
89 10
11 12
13 14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 40
41 42 43 44
45 46
47 48 49 50
51 52 53 54
n (0) H (1)
He (2)Li (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
Ne (10)Na (11)
Mg (12)Al (13)Si (14) P (15)
S (16)Cl (17)Ar (18) K (19)
Ca (20)Sc (21)
Ti (22) V (23)
Cr (24)Mn (25)
Fe (26)Co (27)
Ni (28)Cu (29)
Zn (30)Ga (31)
Ge (32)As (33)
Se (34)Br (35)
Kr (36)Rb (37)
Sr (38) Y (39)
Zr (40)Nb (41)
Mo (42)Tc (43)
Ru (44)Rh (45)Pd (46)Ag (47)
Cd (48)In (49)
Sn (50)
Burst Ignition: Combined H-He runaway
Prior to ignition : hot CNO cycle ~0.20 GK Ignition : 3%
: Hot CNO cycle II!
~ 0.68 GK breakout 1: 15O(,) ~0.77 GK breakout 2: 18Ne( ,p)
(~50 ms after breakout 1) Leads to rp process and main energy production
0 1 23 4
5 6
7 8
9 10
111213
14
1516
17181920
2122
2324
25262728
2930
3132
33343536
3738394041
424344
45464748
49505152
535455
56
5758
59
H (1)He (2)Li (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
Ne (10)Na (11)
Mg (12)Al (13)Si (14) P (15)
S (16)Cl (17)
Ar (18) K (19)
Ca (20)Sc (21)
Ti (22) V (23)
Cr (24)Mn (25)
Fe (26)Co (27)
Ni (28)Cu (29)
Zn (30)Ga (31)
Ge (32)As (33)
Se (34)Br (35)Kr (36)Rb (37)
Sr (38) Y (39)
Zr (40)Nb (41)
Mo (42)Tc (43)
Ru (44)Rh (45)Pd (46)Ag (47)
Cd (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
3 reaction
p process: 14O+ 17F+p 17F+p 18Ne 18Ne+ …
rp process: 41Sc+p 42Ti +p 43V +p 44Cr 44Cr 44V+e++ e 44V+p …
Wallace and Woosley 1981 Hanawa et al. 1981 Koike et al. 1998 etc
Schatz et al. 2001 (M. Ouellette) Phys. Rev. Lett. 68 (2001) 3471
Models: Typical reaction flows
Schatz et al. 1998
0 1 23 4
5 6
7 8
9 10
111213
14
1516
17181920
2122
2324
25262728
2930
3132
33343536
3738394041
424344
45464748
49505152
535455
56
5758
59
H (1)He (2)Li (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
Ne (10)Na (11)
Mg (12)Al (13)Si (14) P (15)
S (16)Cl (17)
Ar (18) K (19)
Ca (20)Sc (21)
Ti (22) V (23)
Cr (24)Mn (25)
Fe (26)Co (27)
Ni (28)Cu (29)
Zn (30)Ga (31)
Ge (32)As (33)
Se (34)Br (35)Kr (36)Rb (37)
Sr (38) Y (39)
Zr (40)Nb (41)
Mo (42)Tc (43)
Ru (44)Rh (45)Pd (46)Ag (47)
Cd (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
3 reaction ++ 12C p process:
14O+ 17F+p 17F+p 18Ne 18Ne+ …
At still higher T: p process
Alternating (,p) and (p,) reactions: For each proton capture there is an (,p) reaction releasing a proton
Net effect: He burning
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0 1 23 4
5 6
7 8
9 10
111213
14
1516
17181920
2122
2324
25262728
2930
3132
33343536
3738394041
424344
45464748
49505152
535455
56
5758
59
H (1)He (2)Li (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
Ne (10)Na (11)
Mg (12)Al (13)Si (14) P (15)
S (16)Cl (17)
Ar (18) K (19)
Ca (20)Sc (21)
Ti (22) V (23)
Cr (24)Mn (25)
Fe (26)Co (27)
Ni (28)Cu (29)
Zn (30)Ga (31)
Ge (32)As (33)
Se (34)Br (35)Kr (36)Rb (37)
Sr (38) Y (39)
Zr (40)Nb (41)
Mo (42)Tc (43)
Ru (44)Rh (45)Pd (46)Ag (47)
Cd (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
The Sn-Sb-Te cycle
104Sb 105Sb 106 107Sb
103Sn 104Sn 105Sn 106Sn
105Te 106Te 107Te 108Te
102In 103In 104In 105In
(γ,a)
Sb
β+(p, )γ
Known ground state emitter
Endpoint: Limiting factor I – SnSbTe Cycle
Woosley et al, ApJS, 151, 175 (2004)
Reaction network (only nuclei indicated with red triangles have
experimetally determined masses)
3 increases Z
Times offset by 41,700 s of accretion at 1.75 x 10-9 solar masses/yr
Z=Z / 20Peak luminosity
approximately Eddington
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8
6 -3
at the base9.07 10 K1.44 10 gm cm
×× beginng of
second burst
note residual carbon
Fourteen consecutive flashes. The first is a start up transient.
M = 1.75×10−9 M
yr-1
Z = Z
/ 20
Subsequent flashes were less violent “Thermal inertia”
GS 1826-24
Heger, Cumming, Gallaoway and Woosley (2005, in prep)
Model A3
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Current Issues:
• What is the physical nature of “superbursts”? Are they carbon runaways? How to accumulate the carbon. Further evolution of ashes
• Detailed comparison with an accumulating wealth of observational data, especially time histories of multiple bursts and the effects of thermal inertia
• Large volume of uncertain, yet important reaction rates (FRIB)
• Multi-D models with B fields and rotation – spreading of the burning
• Can XRB’s be used to obtain neutron star radii, crustal structure, and/or distances
ApJ, 752, 150 (2012)
About 2 dozen superbursts have been observed. They are thought to be produced by carbon runaways as predicted by Woosley and Taam (1976). The fine structure in the above simulation has not yet been observed
“Superbursts”
Recent 2D simulations from Chris Malone using MAESTRO
XRB models by Alex Heger et al.